FTest for Variance Comparison from Independent Samples We have two independent s

Question

FTest for Variance Comparison from Independent Samples We have two independent samples randomly drawn from two normally distributed populations. Some information on the two samples is as follows: n1 = 23 s1 = 5.2 n2 = 19 s2 = 4.7 Let 1 and 2 be population variances. a) Test H0: 1 = 2 versus H1: 1 2 at the 0.025 significance level. b) Determine the pvalue for the test. Hint: Round off probabilities and values to 5 decimal places. Determine probabilities based on some Excel probability and value lookups:

Explanation / Answer

Testing the Difference Between Two Variances
Null Hypothesis, There Is No Significance between them Ho: ^2 = ^2
Alternate Hypothesis, There Is Significance between them H1: ^2 != ^2
Test Statistic
Sample 1
s1^2=27.04, n1 =23
Sample 2
s2^2 =22.09, n2 =19
Fo =27.04/22.09 = 1.22408
| Fo | =1.22408
Critical Value
The Value of |F | at LOS 0.025 with d.f F(n1-1,n2-1)=F(22,18) is 2.908
We got |Fo| =1.224 & | F | =2.908
Make Decision
Hence Value of |Fo | < | F | and Here we Do not Reject Ho

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